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http://dx.doi.org/10.14317/jami.2011.29.5_6.1525

BOOLEAN RANK INEQUALITIES AND THEIR EXTREME PRESERVERS  

Song, Seok-Zun (Department of Mathematics, Jeju National University)
Kang, Mun-Hwan (Department of Mathematics, Jeju National University)
Publication Information
Journal of applied mathematics & informatics / v.29, no.5_6, 2011 , pp. 1525-1532 More about this Journal
Abstract
The $m{\times}n$ Boolean matrix A is said to be of Boolean rank r if there exist $m{\times}r$ Boolean matrix B and $r{\times}n$ Boolean matrix C such that A = BC and r is the smallest positive integer that such a factorization exists. We consider the the sets of matrix ordered pairs which satisfy extremal properties with respect to Boolean rank inequalities of matrices over nonbinary Boolean algebra. We characterize linear operators that preserve these sets of matrix ordered pairs as the form of $T(X)=PXP^T$ with some permutation matrix P.
Keywords
Boolean algebra; Boolean rank; linear operator; (P,Q,B)-operator;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
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